It is already known (cf. [1]}) that in the case of \(S\ge 2\) , the maximal principle holds, i.e., \(\Vert u^n\Vert _\infty \le 1\) .
Multiplying (REF ) by \((u^{n}-u^{n-1})\)  and integrating the equation over \(\Omega \) , we have
\(\frac{1}{\gamma }\langle \overline{\partial }_t^\alpha u(t_n), u^n-u^{n-1}\rangle = \langle \varepsilon ^2\Delta u^{n} -f(u^{n-1})-S(u^n-u^{n-1}),u^n-u^{n-1}\rangle \) 
